Q:

What is the GCF of 70 and 72?

Accepted Solution

A:
Solution: The GCF of 70 and 72 is 2 Methods How to find the GCF of 70 and 72 using Prime Factorization One way to find the GCF of 70 and 72 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here: What are the Factors of 70? What are the Factors of 72? Here is the prime factorization of 70: 2 1 × 5 1 × 7 1 2^1 × 5^1 × 7^1 2 1 × 5 1 × 7 1 And this is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 70 and 72 by multiplying all the matching prime factors to get a GCF of 70 and 72 as 4: Thus, the GCF of 70 and 72 is: 4 How to Find the GCF of 70 and 72 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 70 and 72 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above. Let’s take a look at the factors for each of these numbers, 70 and 72: Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 70 and 72 would be 2. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 65 and 28? What is the GCF of 122 and 49? What is the GCF of 52 and 7? What is the GCF of 110 and 135? What is the GCF of 145 and 84?